Topology of discrete groups and growth series

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400086
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: University of the Ryukyus (2016); Kyoto University (2014-2015)
• Principal Investigator: Fujii Michihiko 琉球大学, 理学部, 教授 (60254231)
• Co-Investigator(Renkei-kenkyūsha): SATOH Takao 東京理科大学, 第二理学部, 講師 (70533256) ; KAWAZUMI Nariya 東京大学, 大学院数理科学研究科, 准教授 (30214646) ; SAITO Kyoji 東京大学, 数物連携宇宙研究機構, 主任研究員 (20012445)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 増大級数 / 有限生成群 / 有理関数表示 / トーラス結び目群 / ケーリー・グラフ / オートマトン

Outline of Final Research Achievements

The head investigator Fujii obtained several results concerning the growth series for a group G(p,q),
which is determined if arbitrary integers greater than or equal to two, p and q, are given.
First, Fujii described a necessary and sufficient condition for a representative of an element g of G(p,q) to be shortest among all representatives of g. Next, Fujii gave a rational function expression for the spherical growth series for G(p,q). Moreover, Fujii constructed a finite state automaton which accepts all of the shortest representatives of G(p,q), and obtained a rational function expression for the geodesic growth series for G(p,q).

Free Research Field

位相幾何学